Sunday, January 28, 2007

As can be seen from the little logo I made, today is the fifth anniversary of the launching of the Hot Hand website. Fittingly, as I'm putting the finishing touches on this write-up, the Phoenix Suns (whose game against Cleveland I've had on in the background) have just won their 17th straight game!

In addition to all the intrinsic fun, operating the site has brought me into contact with a number of sports-minded statisticians and decision researchers, as well as sports reporters, that I don't think I would have met otherwise (see photo on this page). Numerous people have been very supportive of my efforts over the years, which I greatly appreciate. I would like to cite two individuals in particular, one from academia and the other from the baseball world, for lending their gifts to the page.

One is Professor Tom Gilovich of Cornell University, a co-founder of hot hand research (Gilovich, Vallone, & Tversky, 1985, Cognitive Psychology), who was the guest for the first-ever hot hand chat, in 2002. The other is prolific baseball analyst and writer Bill James, who contributed an original study on George Brett and Tony Gwynn to the site in 2005, and has sent along additional commentaries as well.

With my June 2006 switch to the present blog format, documents archived at my previous site (such as those related to Tom and Bill) are no longer available online; I've saved electronic copies, though, so if you're interested in these, please e-mail me via the link to my faculty webpage.

To mark this anniversary, I thought I'd summarize what I think are some of the biggest new developments in hot hand research over the past five years (the summaries below alternate in red and in black font, to set them apart visually). If you have additional suggestions or want to discuss one of the areas I've raised, please submit a comment via the link at the bottom of this write-up.

*Whereas my (and others') analyses of events such as the NBA All-Star Long-Distance Shootout (three-point shooting contest) and MLB All-Star Home Run Derby still have not found much evidence for the probability of a success following a success exceeding the probability of a success following a failure, there have been findings of streakiness in other sports.

The chances of detecting streakiness would seem to be enhanced when players could execute a short, simple motion (e.g., swing or stroke) in relation to the ball, which could be repeated often and in short succession. That way, a player could rehearse and remember how he or she executed a successful motion and apply it repeatedly. Consistent with this reasoning, recent studies have shown some evidence of hot hands in bowling (Dorsey-Palmateer & Smith, 2004, The American Statistician), tennis (Klaassen & Magnus, 2001, Journal of the American Statistical Association), and golf putting (Gilden & Wilson, 1995, Psychonomic Bulletin & Review).

*The realization that the athletes who are the most likely to go on hot streaks are those who already have among the highest percentages of success in their respective sports (think Joe DiMaggio's 56-game hitting streak or Tiger Woods's 142-tournament streak of always making the cut) has some interesting implications. One of them is that it may be optimal after all to pass the basketball to a player on a hot streak -- not because making shots increases that player's shooting percentage on future shots above his or her typical percentage, but because the player on a hot streak is likely to be the team's best shooter overall. Bruce Burns, who published a study making this point in Cognitive Psychology in 2004, was kind enough to elaborate upon this theme in an online chat with us a few years ago.

*Streakiness analyses have also provided a vehicle for advances in basic statistics. Klaassen and Magnus (2001) concluded their aforementioned analysis of tennis, which found a positive correlation between winning the previous point and the current one, thusly: "In addition to the empirical findings on tennis, the paper provides a theoretical contribution to the estimation of discrete dynamic panel data models."

*The 2001 baseball book Curve Ball, whose authors Jim Albert and Jay Bennett also participated in an online chat, introduced me to what, for me, was a non-traditional form of analysis, namely visual comparisons based on simulations. I've used this technique a few times over the years, including a 2002 examination of whether Natalie Ritchie and Amber Tarr, two women's basketball players from my home university, Texas Tech, showed any evidence of streakiness in their three-point shooting.

The main idea from Albert and Bennett was to use a spinner, similar to that in the old board game All-Star Baseball, to demonstrate that even an event-generator with the same underlying probability throughout can produce "streakiness" of hot and cold. An example for Ritchie is shown below. Because Ritchie was a 37% three-point shooter overall, I simulated a spinner by obtaining a series of random numbers between 1-100 (each random number corresponded to each shot she actually took during the season). Each random number was examined, in sequence. If a random number were between 1-37 (corresponding to her 37% success rate), it was considered a made three-pointer, whereas a number between 38-100 was considered a miss.

As can be seen, even with the simulated spinner that we know to have a consistent 37% hit rate on each shot, the simulated sequence showed rises and falls, similar to Ritchie's actual shooting (although the rises and falls were not necessarily located in the same places in the two versions).

*The above illustration of visual analysis sets the context for what is perhaps my favorite streak-related story during my time operating this website. In the middle-late part of Big Ten play in 2006, Ohio State's Je'Kel Foster (isn't that a perfect name for someone who goes hot and cold in his shooting?) had an amazingly hot stretch, followed by an equally amazing cold stretch.

First, take a look at this lovely graph from Buckeye Commentary (below the two pie-charts on the new page that comes up). What you'll see is that Foster was consistently shooting (roughly) at a mind-boggling 80% clip during a three-game stretch. This was then followed by a six-game stint in which his average 3PT% was in the teens!

Given Foster's 40% overall 3PT% from behind the arc last season, it certainly appears that his actual highs were higher than what would be expected by chance, and his actual lows were lower.

*Whereas the evidence for individual basketball players' streakiness (beyond chance) appears weak, a promising area that has some preliminary support is that of team runs. The term, inspired by then-Kansas coach Roy Williams's 2003 assertion that, "We are a team of runs," refers to instances where one team handily outscores the other during a stretch, such as the Purdue men going on a 21-0 run yesterday against Illinois (see my posting below from yesterday).

I again used the simulated-spinner approach, although somewhat differently than in the above example. I focused on the unique rivalry between Kansas and Arizona in '03, in which the teams met twice (once in the regular season and once in the NCAA tournament) and both games were laden with team runs. Using data from the entirety of both real games between the teams, I made "possession spinners" for each team (separately). For each team, I calculated the actual, empirical percentage of possessions on which they scored 0, 1, 2, or 3 points, in the two games combined. A team's "spinner" would thus have a no-point area exactly proportional to the team's actual frequency of scoring no points on a possession, a 1-point area proportional to the team's frequency of scoring one point, etc.

I then created some simulated games between the teams, where I would alternate spinning one team's spinner and then the other's, with the number of spins based on the actual number of possessions in the two KU-UA games. The idea, again, is that even though the spinner used for each team is consistent from possession to possession (and includes ample opportunity for scores and non-scores), random processes (e.g., unusually long streaks of scores by one team and non-scores by the other) could still cause team runs to occur. The key question is how these chance-based simulated team runs compared to the actual team runs in the two KU-UA games.

I concluded that:

"Overall, 12 shut-out runs of 7-0 or greater were observed in the 5 simulated games, for an average of 2.4 per game. The frequency of these runs seemed pretty comparable to those observed in the actual KU-UA games. However, the magnitude levels of the runs were largely higher in the actual games (e.g., 11-0, 12-0, 13-0, and 16-0) than in the simulations of chance/independence."

*A final potential research area, still in its early stages, involves integrating streakiness with such potentially related topics as clutch performance and choking. Such was the basis for an online chat with Russ Clark, who had conducted extensive statistical studies of professional golf performance. During the preparations for Dr. Clark's chat, we were pleased to receive a question from Sian Beilock, a prominent scholar of "choking" and mental processes in skilled performance more generally. Dr. Beilock gave a colloquium at Texas Tech this past October, and I was able to go up afterwards and introduce myself.

*Lastly, I want to address a more epistemological point. Something for which I've occasionally been called on the carpet and on which I'm trying to improve, is the need for greater contextualization of findings in terms of the opportunities for something to occur. Statistically analyzing events that captured our attention in the first place precisely becauseof their unusual nature, after the fact, and increasing the number of preconditions (e.g., how likely was Event A to occur, given that unusual events B, C, and D had already occurred?) all have the potential to make the events I analyze seem more rare than they really are. When considering the large numbers of games played each year in a given sport or league, and the many years these leagues have been in existence, it sometimes turns out that what appears to be a highly rare occurrence really isn't, given the big picture of the numerous opportunities for such an event to occur.

On the other hand, sometimes the events we see really are inordinately rare, using any reasonable standard. After the Wake Forest men's basketball team made 50 straight free throws in January 2005, analyst Ken Pomeroy concluded the following:

Assuming Wake Forest shoots 25 free throws a game, you would expect this event to happen to the Deacons once in every 66,000 games...2,200 seasons...110 generations.

I hope you've found my analyses (as well as those by others) to be informative, thought-provoking, and entertaining. If so, I hope to continue my streak of writing up worthwhile analyses for as long as possible.